# Analog PLL- elementary question

#### gary36

##### Full Member level 2
Just started refreshing PLL concept in the context of demodulation of FM signal. Taking the digital PLL first, phase sensitive detector is typically XOR gate. So my guess was that the output of VCO must be same as incoming signal Fin to produce zero output from XOR detector. In that case Fvco should be equal to Fin. Is that correct?The output of PLL must be the message signal.

#### KlausST

##### Super Moderator
Staff member
Hi,

Somehow correct and somehow not.

Only with a closed control loop you get Fvco = Fin.
But the XOR output is not necessarily 0 when both frequencies are equal.
The averaged XOR output depends on phase shift. It is 0 when phase shift is 0°
It will be 50% VCC when phase shift is 90° or 270°
It will be 100% VCC when phase shift is 180°

When both frequency differ the low pass filtered output gives a symmetric triangle signal 0V to VCC with f = |fin - fvco|

Klaus

#### Easy peasy

read the CD4046 data sheet - gives good insight ...

Classic application book -

A more indepth look -

Regards, Dana.

#### gary36

##### Full Member level 2
Hi

For analog PLL with VCO producing sine wave, I found (in simulation) that VCO frequency always matches with the carrier frequency. By the way If I can fix the local oscillator frequency equal to carrier frequency, I can still recover message signal. Why then closed loop feedback is required?

I must be missing something, I thought the very definition of a PLL
includes fdbk ?

Regards, Dana.

#### gary36

##### Full Member level 2
Hi Dana

If we multiply FM signal by carrier frequency and pass it through LPF, We can get the message signal. Similar to coherent detection in AM demodulation. So what's the point of feedback?

#### Easy peasy

since it is a loop - the o/p of the VCO is " fed back " to the phase detector to complete the loop ...

#### FvM

##### Super Moderator
Staff member
If we multiply FM signal by carrier frequency and pass it through LPF, We can get the message signal. Similar to coherent detection in AM demodulation. So what's the point of feedback?
That's a rather superficial description, you hardly get a working FM detector this way. How do you generate the correct carrier frequency? What's the relevance of carrier phase?

By the way If I can fix the local oscillator frequency equal to carrier frequency, I can still recover message signal. Why then closed loop feedback is required?
In practice, the feedback loop is required to "fix" the LO frequency and phase-lock it to the carrier.

#### gary36

##### Full Member level 2
I get the point. We are considering feedback for compensating phase shift errors in carrier signals

#### betwixt

##### Super Moderator
Staff member
... and it is the instantaneous ERROR voltage correcting the phase difference that recovers your modulation. The loop filter generally has a long time constant (makes it slow to respond) to align the signal and LO phases but the more rapid changes match the original modulating signal.

Brian.

#### gary36

##### Full Member level 2
But I was just experimenting in simulink and I found that when I assign VCO free running frequency equal to carrier frequency, only then I get correct output from the Low pass filter, that is the message signal. Why this is so. I was thinking that feedback loop will adjust itself to generate the correct VCO output

#### KlausST

##### Super Moderator
Staff member
Hi,
I assign VCO free running frequency equal to carrier frequency
but that´s the key point.
You may do this in simulation, but not in reality. In simulation you are able to set both frequencies to be equal. But in reality you are not.
Let´s say you have a 100MHz carrier. And "your" free running VCO is just 10ppm off, then the frequency difference is 1kHz.
1kHz offset.
Let´s say the transmitter input is zero then your low pass filtered "received" signal will become 1kHz.
Let´s say the transmitter input is 5kHz then your low pass filtered "received" signal will become 4kHz (or 6kHz).
Voice will be no longer voise. You won´t understand a word.

Now you may say one may "adjust" or "sync" the frequency from time to time. Then you need to do this relatively often, else the frequency will drift and the sound will be awful.
The only option is to "sync" it continously.
--> it is not free running anymore. It is feedbacked, a loop. A phase loocked loop.

Klaus

#### gary36

##### Full Member level 2
Hi KlausST

The purpose of feedback is clear. But should I set the free running frequency and sensitivity of VCO same as the transmitted signal. This means I should be aware of the signal characterstics recieved. Is it true? I wonder how would single PLL behave,when when we have multi tone signals?

#### FvM

##### Super Moderator
Staff member
What are you asking about, multiple carrier frequencies or multi tone modulation signal? In the latter case, there would be still a single constant carrier frequency.

But generally speaking, we need a signal specification to discuss if and how a PLL can lock to it.

#### gary36

##### Full Member level 2
Ok. Let us say we have the latter case (multi tone modulation) where carrier frequency is constant. Now how do we fix the sensitivity of VCO ?
This is because different tones can have varying sensitivites ( 1st one might have 20Hz/V, while the 2nd may have 50Hz/V). Now when we say lock, do we mean that VCO output is an FM signal? In simulation VCO output is the carrier frequency. This is still unclear because phase detector must null the loop. For this condition VCO output must be FM ,in sync with input.

#### KlausST

##### Super Moderator
Staff member
Hi,

I assume you are mixing several things.
"FM" means that there is a analog signal input ... and according this input level (amplitude) the output frequency (of the carrier) is modified.

A simplified example - without knowing whether the values are realistic or not (modulation factor: 1V --> 20kHz)
Let´s say you have a carrier of 100MHz.
And you have a
* 0V analog signal input then the (modulated) output frequency is 100.000MHz
* -1V input then the output is 100.000MHz - 20kHz = 99.980MHz
* +1V input then the output is 100.000MHz + 20kHz = 100.020MHz
* +0.1V input then the output is 100.000MHz + 2kHz = 100.002MHz
.. and so on

In a non feedbacked system the low pass filtered XOR ouput in the demodulator gives the difference frequency
BUT: in a feedbacked system the low pass filtered XOR output gives the amplitude information.

*****

Another "picture" to visiualize the FM transmitter and receiver:

Let´s say you have an FM transmitter: simplified this is a VCO. At zero input there is 100MHz ouput. ...and so on, like the example above.
Now let´s say you have an identical VCO at the receiver. It´s output freuqency needs to follow the transmitter frequency.
Don´t think about "how" this is achieved for now...just generally:
* if the transmitter VCO frequency is 100.000MHz then the receiver VCO frequency needs to be 100.000MHz, too
* if the transmitter VCO frequency is 100.020MHz then the receiver VCO frequency needs to be 100.020MHz, too
* if the transmitter VCO frequency is 99.980MHz then the receiver VCO frequency needs to be 99.980MHz, too

* for 100.000MHz output it needs 0V input
* for 100.020MHz output it needs +1V input
* for 99.980MHz output it needs -1V input
--> So the reciever VCO input is identical to the transmitter VCO input. Somehow.
In other words: The receiver VCO analog input is the demodulated signal = the output signal. (voice, audio...)

now back to the "HOW":
There is the XOR. It´s output gives an information about the phase shift between transmitter frequency and receiver frequency.
As soon as there is a phase shift "detected" it ... this information is used as analog VCO input to make it compensate the phase shift: or: to adjust the VCO frequency.
-->Due to the feedback there will be no "true" frequency difference between transmitter VCO frequency and receiver VCO frequency, just some "lag" or "lead" in phase.

Klaus

Hi KlausST

The purpose of feedback is clear. But should I set the free running frequency and sensitivity of VCO same as the transmitted signal. This means I should be aware of the signal characterstics recieved. Is it true? I wonder how would single PLL behave,when when we have multi tone signals?
Capture and Lock range are a f() of loop gain and LPF characteristics. So no, you dont have to set
the VCO to xmitted freq. The loop will "acquire" the signal. Keep in mind there are other considerations
when discussing capture range, like noise environment.

See Gardner equations, and a revised paper, below, for capture range and lock range calculations -

Regards, Dana.